What Field Involves Derivatives and Integrals with Respect to Vectors?

[CuppoJava]

Hi,
I'm reading through a probability textbook right now (Pattern Recognition and Machine Learning by Bishop) and it makes heavy use of "vector calculus".

"Vector Calculus" is in quotations, because it's unlike the vector calculus that I learned in my courses (gradients, curls, divergence, etc...).

There's lots of formulas where he literally takes the derivative of a function with respect to a vector. Or he integrates a formula with respect to a vector.

What field of mathematics is this? And are there any good books where can I learn more about it?

Thanks
-Patrick

 

[Dragonfall]

Sounds exactly like "vector calculus", the way it should be. For a good textbook see http://www.chapters.indigo.ca/books/Vector-Calculus-Jerrold-E-Marsden/9780716749929-item.html?ref=Search+Books:+%2527vector+calculus%2527

 

[CuppoJava]

Thank you for your help, I'm on my way to the library right now to get a copy of it.

As an aside then, are the Curl, Gradient, and Divergence properties also part of vector calculus? I scoured the internet for hours looking for the definition of an integral with respect to a vector, but the only results I came up with concerning "vector calculus" was regarding those three operators and their properties.

 

[Gear300]

Thank you for your help, I'm on my way to the library right now to get a copy of it.

As an aside then, are the Curl, Gradient, and Divergence properties also part of vector calculus? I scoured the internet for hours looking for the definition of an integral with respect to a vector, but the only results I came up with concerning "vector calculus" was regarding those three operators and their properties.

yup, they are.